Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Pierce, Lillian B."'
Autor:
Chu, Rena, Pierce, Lillian B.
Let $T_t^{P_2}f(x)$ denote the solution to the linear Schr\"odinger equation at time $t$, with initial value function $f$, where $P_2 (\xi) = |\xi|^2$. In 1980, Carleson asked for the minimal regularity of $f$ that is required for the pointwise a.e.
Externí odkaz:
http://arxiv.org/abs/2309.05872
We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Ha
Externí odkaz:
http://arxiv.org/abs/2212.11038
We provide a simple criterion on a family of functions that implies a square function estimate on $L^p$ for every even integer $p \geq 2$. This defines a new type of superorthogonality that is verified by checking a less restrictive criterion than an
Externí odkaz:
http://arxiv.org/abs/2212.08956
We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by $(y,Q(y))\subseteq \mathbb{R}^{n+1}$, for an arbitrary non-degenerate quadratic form $Q$, admits an a priori bound on $L^p$ for all $1
Externí odkaz:
http://arxiv.org/abs/2211.15865
Autor:
Bonolis, Dante, Pierce, Lillian B.
Publikováno v:
Alg. Number Th. 18 (2024) 1515-1556
Let a polynomial $f \in \mathbb{Z}[X_1,\ldots,X_n]$ be given. The square sieve can provide an upper bound for the number of integral $\mathbf{x} \in [-B,B]^n$ such that $f(\mathbf{x})$ is a perfect square. Recently this has been generalized substanti
Externí odkaz:
http://arxiv.org/abs/2209.02494
Autor:
Pierce, Lillian B.
Each number field has an associated finite abelian group, the class group, that records certain properties of arithmetic within the ring of integers of the field. The class group is well-studied, yet also still mysterious. A central conjecture of Bru
Externí odkaz:
http://arxiv.org/abs/2206.08351
We formulate a general problem: given projective schemes $\mathbb{Y}$ and $\mathbb{X}$ over a global field $K$ and a $K$-morphism $\eta$ from $\mathbb{Y}$ to $\mathbb{X}$ of finite degree, how many points in $\mathbb{X}(K)$ of height at most $B$ have
Externí odkaz:
http://arxiv.org/abs/2109.11167
Publikováno v:
Q. J. Math. 74, no. 1, 139-161, 2023
In this work we study $d$-dimensional majorant properties. We prove that a set of frequencies in ${\mathbb Z}^d$ satisfies the strict majorant property on $L^p([0,1]^d)$ for all $p> 0$ if and only if the set is affinely independent. We further constr
Externí odkaz:
http://arxiv.org/abs/2106.12538
In 1980 Carleson posed a question on the minimal regularity of an initial data function in a Sobolev space $H^s(\mathbb{R}^n)$ that implies pointwise convergence for the solution of the linear Schr\"odinger equation. After progress by many authors, t
Externí odkaz:
http://arxiv.org/abs/2103.15003
Autor:
Pierce, Lillian B.
In this survey, we explore how superorthogonality amongst functions in a sequence $f_1,f_2,f_3,\ldots$ results in direct or converse inequalities for an associated square function. We distinguish between three main types of superorthogonality, which
Externí odkaz:
http://arxiv.org/abs/2007.10249